"One hates an author that's all author," wrote Byron, a great contriver of informality. Diana Athill writes as if she were not an author at all. For many readers of Somewhere Towards the End, part of the book's pleasure is encountering someone who has lived in a literary world, but who has escaped its pretensions. She may have published six books of memoirs and a novel, but she presents herself as someone who has slipped into authorship. (Her publishers might be forgiven a wince when she dismisses her own novel as written "against my better judgment", and proof that "anyone who can write at all can squeeze out one novel at a pinch".) One chapter of this book reflects on the "best part" of her old age: having had "the luck to discover I can write". "Real writers" set themselves to fulfil plans; she has but followed her pleasure. "I am an amateur."

Her style in the book is true to her self-description: she writes unprofessionally. This is not to say that her sentences are awkward or her diction imprecise. Those who have praised her memoir for its stylistic grace and clarity are certainly identifying its qualities. Athill writes with the precision of someone who spent her professional life as a corrector of prose. In Stet, her memoir of her time working for the publisher André Deutsch, she recalls cases in which she had to rewrite whole books, where the author had something to say but wrote inaccurately. She knows better than almost any memoirist what stylistic correctness is.

Whether luckily discovered or cleverly contrived, hers is a prose of educated informality. Some of its signs are small. She uses contractions such as "can't", "shouldn't", "didn't" as if she were conversing. She inserts little phrases that are common in conversation but usually purged from professional prose: "And another thing", "to be more serious", "I suppose", "so to speak". And, despite her sophisticated syntax, speech is what she seems to achieve. Without misgivings, she uses idiomatic exclamations. To dig up all her "past guilts" would be "a great bore". (A bore for the reader, it is implied, because a bore for herself.) The old-fashioned phrase makes what would seem evasion in another memoirist feel like consideration in her. When she remembers her one sight of a dead body, the corpse of her employer's mother, whom she had been asked to identify, her description characteristically turns to a genteel colloquialism. There was "poor little Maria", looking "as though she were in a state of great bewilderment and dejection because something too unkind for words had been done to her". No serenity or reassurance here, but "something too unkind for words". It is a brilliantly unsettling use of that slightly antique idiom, for indeed words are not up to what death has done.

She is not afraid to use clichés for common experiences. People "keep their wits about them". A relationship "was going to end in tears". Many people are determined to give the world their novels "come hell or high water". She remembers her old and ailing mother declaring that she was not afraid of death, and believes that she spoke the truth. Yet though the same may be true of herself, "there are words which follow that statement so often that they have become a cliché: 'It's dying that I'm afraid of'." "When dying is actually in sight," she observes, "those words become shockingly true." The well-worn turn of phrase has been worn for a good reason.

The refusal to avoid phrases that others have used before is a kind of courtesy to the reader, as is the refusal to remember everything. Athill recalls John Updike "analysing (I don't remember where) his own religious belief". Having known and edited many famous writers, she has earned the right to be casual about provenances. But such studied negligence is also what earns her credibility. Most memoirs are distinguished by unflagging recollection. Many provide substantial chunks of dialogue, incredible by the standards of our usual capacity to remember what anyone has said yesterday, let alone years before. Yet we accept it as a convention of autobiographical narrative. Athill, in contrast, cannot remember everything. She will preserve a habitual turn of phrase - Jean Rhys's "I was a bit drunk, well very" - but never pretends to reanimate passages of conversation. At one point she includes entries from a diary kept while she was looking after her former lover, Barry. Here, you might think, is the full record of the past. But characteristically, the first entry begins, "I can't remember ..."

• John Mullan is professor of English at University College London. He will be talking to Diana Athill about her memoir on Wednesday 11 March at 7pm in the Scott Room, The Guardian, Kings Place, 90 York Way, London N1. Returns only from book.club@theguardian.com or call 020 3353 2881.